Google’s smart home speakers on Thursday played an unprompted promotion for Walt Disney Co.’s new “Beauty and the Beast” movie, the first sign of how the world’s largest advertising company could shoehorn ads into its growing number of voice interactions with users.

Users of Google’s voice-controlled speaker, called Google Home, heard a 17-second promotion for the movie, after asking the devices about the their schedule. “By the way, Disney’s live-action Beauty and the Beast opens today,” the device said, according to...